For example:
Suppose I told you it was 10:00 a.m.  What time is it 6 hours from now? ___________

The time you use everyday is a cycle of 12 hours, divided up into a cycle of 60 minutes.
For every time you pass 12, you start over with 1 again.  This is "mod 12" arithmetic. 

Let's set up a picture.

You put 0 through 11 in a circle.  Then to figure out what the answer to a modular math question, you begin at 0 and count around the clock a certain amount of times.  The number you end up on is the answer.

Example:
We want to calculate 32 (mod 12). We start at 0 and go all the way back to 0. This uses up 12 of the hours. We have 32-12 =20 left. We go around again. We have 20-12 = 8 left. Therefore 32 (mod 12) is equal to 8.

What about 27 mod 12? ______________

What about 155 mod 12? ______________

Question:  Why do you think we label the clock 0 through 11, instead of 1 through 12?


Okay, now try 155 mod 12 again. _______________

1. It would be "mod ____" if we did minutes instead of hours.
   
   
   
   
2. What about if we did military time?
   
   
   
   
3. Where would the minute hand be 342 minutes from 10:00?
   
    
   
   
4. What time would it be (including the hour) for problem 3?
   
   
   
   
5. If it is now 9:43, what time would it be in 200 minutes?
   
   
   
   
6. What month would it be 43 months from now?
   
   
   
   
7. What day of the week would it be 53 days from now?
   
   
   
   
8. If it is 11:00 right now, what time was it 76 hours ago?
   
   
   
   
9. BONUS: Try to figure out which day of the week you were born on.